The sequence of numbers, 7, 10, 17, 27, 44, 71, 115... in which each new term is given by the sum of the previous two terms, gives the sum of the first 10 terms as 1,265
What is a sequence of numbers?A number sequence consists of a listing of numbers that are connected to each other by a rule.
The given sequence is presented as follows;
7, 10, 17, 27, 44, 71, 115..., [tex] a_{10}[/tex]
From the given sequence, we have;
a_n = a_{(n-1)} + a_{(n-2)}
The first 10 terms of the sequence is therefore;
7, 10, 17, 27, 44, 71, 115, (71+115), (115+(71+115)), ((71+115)+(115+(71+115)))
Which gives;
7, 10, 17, 27, 44, 71, 115, 186, 301, 487
The sum of the first 10 terms of the sequence is therefore;
7 + 10 + 17 + 27 + 44 + 71 + 115 + 186 + 301 + 487 = 1265
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What is the volume of this sphere? Use : 3.14 and round your answer to the nearest hundredth. 9 yd cubic yards
3,058.08 cubic yards
Explanation:radius = 9 yd
π = 3.14
Volume of a sphere = 4/3 πr³
Volume of sphere = 4/3 × 3.14 × 9³
Volume of sphere = 3052.08
To the nearest hundredth, the volume 3,058.08 cubic yards
-13x-2x + 3 = -5x - 17
Answer:
-15x - 3
I hope this helps :)
can anyone help me pls?
1. Which kind of model do you think best represents the profit for each business?
2. Find a function that models the profit you can expect, based on your projections, for each business. You can round your values to the nearest thousandth, as needed.
Lawn care is kind of model do you think best represents the profit for each business.
What is profit?
The financial gain a business has when revenue exceeds costs and expenses is repeatedly alluded to as profit. One cup of lemonade, for instance, costs a child at a lemonade stand one quarter. She then charges $2 for the drink. She made $1.75 in profit just on cup of lemonade.Dog walker = 5 + 12 + 23 + 50 + 62 + 82 = $234
House sitter = 11 + 19 + 29 + 38 + 50 + 73 = $220
Lawn care = 142 + 150 + 165 + 141 + 120 + 91 = $809
Lawn care is kind of model do you think best represents the profit for each business.
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The equation for line A is given by y = 1/2 x + 4 suppose line A is parallel to line B and line T is perpendicular to line A point (- 3, 1) lies on both lineB and liner T. Part A write an equation for line B Part B Write an equation for line T
We will find lines B &
Express (23)−2 using exponents
The expression as an exponent is 21^1
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to evaluate the expression?The expression is given as
(23) - 2
Open the bracket in the above expression
So, we have the following equation
(23) - 2 = 23 - 2
Evaluate the difference in the above expression
So, we have the following equation
(23) - 2 = 21
The above expression can be rewritten as
(23) - 2 = 21^1
Hence, the equivalent expression is 21^1
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What is an expression equivalent to 5(32) using the distributive property?
Drag and drop the appropriate number into each box.
2 5 10 12 30 500
Answer:
The answer is 5(30+2)!
Can someone please help me with this? THANKS!
Answer:
I think it's 171.5 in^3 but not sure :)
Step-by-step explanation:
Factorise:
x² + 6x - 16
Answer:
(x-2)(x+8)
Step-by-step explanation:
Question 1
In each pair, some of the angles of two triangles in degrees are given. Use the
information to decide if the triangles are similar or not. Explain how you know.
Triangle A: 53, 71,; Triangle B: 53, 71,
• Triangle C: 90, 37,______; Triangle D: 90, 53,
• Triangle E: 63, 45,; Triangle F: 14, 71,
Triangle G: 121,____________; Triangle H: 70,
●
●
-
The equality of the respective angles and the proportionality of the corresponding sides determine if two triangles are comparable.
Triangle A: 53, 71, Triangle B: 53, 71; Similar
Triangle C: 90, 37, Triangle D: 90, 53; Similar
Triangle E: 63, 45 Triangle F:14, 71; Not similar
Triangle G, 121, Triangles H: 70, Not similar
If two of one triangle's angles are congruent with two of the
angles of a different triangle, then the two triangles are comparable.
Similarity hypothesis, angle, and AA
Given that: The interior product of the AA similarity hypothesis
The angle sum property of a triangle states that the angles of a triangle are 180°,
Consequently, the third angle is also congruent when two angles are
congruent
53, 71 in Triangle A and 53, 71 in Triangle B; similar
Based on the AA similarity postulate, the triangles are similar.
Triangles C (90, 37) and D (90, 53) have similar angles.
Supplied that the given angles are identical to each of their complimentary angles, the triangle is similar.
Triangle F: 14, 71 Triangle E: 63, 45; not comparable
There are no parallel triangles.
Triangles H: 70, not identical to Triangle G's 121,
The details are insufficient.
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If a=6 and b=4, solve for c using the following equation:
c=√a² + b²
c=√/52
c=20
c=√/20
c=52
Answer:
22
Step-by-step explanation:
1. √a square+b square2.√6 square +4 square3.√36 +164.6+165.22A recent survey was given to determine students favorite school subjects. 6 students chose Math, 3 students chose Science, 4 students chose English and 7 students chose History. Predict the number of students out of 400 that would pick math as their favorite subject
Out of 400 students, 120 students would pick math as their favorite subject.
Data provided to us
fav subject students
Math 6
Science 3
English 4
History 7
Hence the total becomes 20 students
we have to calculate students whose favorite subject is math from 400 students
students with math as fav subject out of 20 students = 6
students with math as fav subject out of 400 students = (6 / 20) x 400
= 120 students
we can verify it as
%age of students out of 20 , who like math = 6/20 x 100
= 30 %
similarly, %age of students out of 400, who like math= 120/400 x 100
= 30 %
As we can see both the percentages are same. and the answer is verified .
So 120 students would pick math as their favorite subject out of 400 students.
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Find m∠1 and m∠2. Tell which theorem can be used.
Answer:
m∠1 = 140 by the Alternate Interior Angles Theorem
m∠2 = 40 by the Consecutive Interior Angles Theorem
Step-by-step explanation:
What is the solution to the inequality x2 + 2x ≤ 24?
Answer:
-6 ≤ x ≤ ∨ x = 4
Step-by-step explanation:
x^2 + 2·x ≤ 24
x^2 + 2·x - 24 ≤ 0
-1 - √(1 + 24) ≤ x ≤ -1 + √(1 + 24)
-1 - 5 ≤ x ≤ -1 + 5
-6 ≤ x ≤ ∨ x = 4
suppose that, in the base period, a college student buys 20 gallons of gasoline at $2 per gallon, 2 mugs for $13 each, and 4 movie tickets for $7 each. in the next month, the price of gasoline is $2.25 per gallon, mugs cost $12.50 each, and the price of a movie ticket is $7.50. the change in the price level from the first to the second month is:
The change in the price level from the first to the second month is 106.4
What is meant by price index?Price index: Price index, measure of relative price changes, consisting of a series of numbers arranged so that a comparison between the values for any two periods or places will show the average change in prices between periods or the average difference in prices between places.
A college student purchases 4 movie tickets for $7 each, 2 CDs for $13 each, and 20 gallons of gasoline at $2 a gallon during the base period.
Gas will cost $2.25 per gallon in the upcoming month, CDs will cost $12.50 each, and cinema tickets will cost $7.50
The price index
=(price in current year/price in last year) x 100
=100/94 x 100
=106.38 or 106.4
The change in the price level from the first to the second month is 106.4
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Please help,
A map of an amusement park is shown on the coordinate plane with the approximate location of several rides.
Determine the distance between the Woozy Wheel and the Roller Rail.
A. 119 units
B. 11 units
C. 169 units
D. 13 units
Answer:
D. 13 units
Step-by-step explanation:
Woozy Wheel: (-14, 1)
Roller Rail: (-2, -4)
[tex] \sqrt{ { - 14 - ( - 2))}^{2} + {(1 - ( - 4))}^{2} } [/tex]
[tex] \sqrt{ {( - 12)}^{2} + {5}^{2} } [/tex]
[tex] \sqrt{144 + 25} = \sqrt{169} = 13[/tex]
The distance between the Woozy Wheel and the Roller Rail is D. 13 units
What is the distance formula between two points?The distance formula between two points (x₁, y₁) and (x₂, y₂) is
D = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
Given, A map of an amusement park is shown on the coordinate plane with the approximate location of several rides.
The point at which Woozy Wheel is (-14, 1) and the point at which Roller Rail
is (-2, - 4).
∴ The distance between the Woozy Wheel and the Roller Rail is,
D = [tex]\sqrt{(-2 + 14)^2 + (-4 - 1)^2}[/tex] units.
D = [tex]\sqrt{(12)^2 + (-5)^2}[/tex] units.
D = [tex]\sqrt{144 + 25}[/tex] units.
D = [tex]\sqrt{169}[/tex] units.
D = 13 units.
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A copy machine makes 126 copies in 3 minutes and 30 seconds. How many copies does it make per minute?
Answer: 36 copies per minute
Step-by-step explanation:
126 copies in 3.5 minutes
We want x number of copies per 1 minute
[tex]\frac{126copies}{3.5minutes} = \frac{xcopies}{1minute}[/tex]
Cross multiply and we get
126 = 3.5x
Solve for x.
x = 126/3.5
x = 36
36 copies per minute
solve for w -5.36=10+w/6
An expression is a collection of variables and constants that are bound by some mathematical operation the value for w for the given expression w -5.36=10+w/6 is 18.432.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
As per the given expression,
w - 5.36 = 10 + w/6
Subtract w/6 both sides,
w - w/6 - 5.36 = 10 + w/6 - w/6
5w/6 = 10 + 5.36
w = 18.432
Hence "The value for w for the given expression w -5.36=10+w/6 is 18.432".
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Describe a series of transformations that takes triangle Q to triangle P.
ANSWER: Translation of Triangle Q to Triangle P
Horizontal shift 4 units left and Vertical shift 1 unit upward
What is the correct notation for a ray with endpoint E
Answer:
There isn't an image to go with your question. repost this question with an image to be able to receive an answer.
Have a nice day :)
Answer:
Step-by-step explanation: You don't have an picture for me to explain add a picture and I'll be able to help you.
The standard form for a parabola with vertex (h,k) and an axis of symmetry of x=h is:(x-h)^2=4p(y-k)The equation below is for a parabola. Write it in standard form. When answering the questions type coordinates with parentheses and separated by a comma like this (x,y). If a value is a non-integer then type is a decimal rounded to the nearest hundredth. 5x^2-50x-4y+113=0 The value for p is: AnswerThe vertex is the point: AnswerThe focus is the point: AnswerThe directrix is the line y=Answer
Given the equation of a parabola:
[tex]5x^2-50x-4y+113=0[/tex]• You can rewrite it in Standard Form by following these steps:
1. Add the y-term to both sides of the equation:
[tex]\begin{gathered} 5x^2-50x-4y+113+(4y)=0+(4y) \\ \\ 5x^2-50x+113=4y \end{gathered}[/tex]2. Subtract the Constant Term from both sides of the equation:
[tex]\begin{gathered} 5x^2-50x+113-(113)=4y-(113) \\ \\ 5x^2-50x=4y-113 \end{gathered}[/tex]3. Divide both sides of the equation by 5 (the leading coefficient)
[tex]x^2-10x=\frac{4}{5}y-\frac{113}{5}[/tex]4. The coefficient of the x-term is:
[tex]b=-10[/tex]Then, you need to add this value to both sides:
[tex](\frac{-10}{2})^2=5^2[/tex]Therefore.
[tex]\begin{gathered} x^2-10x+5^2=\frac{4}{5}y-\frac{113}{5}+5^2 \\ \\ x^2-10x+5^2=\frac{4}{5}y+\frac{12}{5} \end{gathered}[/tex]5. Rewrite the equation as follows:
[tex]\begin{gathered} (x-5)^2=\frac{4}{5}(y+3) \\ \\ (x-5)^2=0.8(y+3) \end{gathered}[/tex]• Having the equation written in Standard Form:
[tex](x-h)^2=4p(y-k)[/tex]You can identify that:
[tex]4p=\frac{4}{5}[/tex]Solving for "p", you get:
[tex]p=\frac{4}{5\cdot4}=\frac{1}{5}=0.2[/tex]• You can identify that:
[tex]\begin{gathered} h=5 \\ k=-3 \end{gathered}[/tex]Therefore, the Vertex is:
[tex](5,-3)[/tex]• By definition, the Focus of a parabola that opens upward is given by:
[tex](h,k+p)[/tex]Then, in this case, this is:
[tex](5,-3+0.2)=(5,-2.8)[/tex]• By definition, the Directrix for a parabola that opens upward is given by:
[tex]y=k-p[/tex]Then, in this case, you get:
[tex]\begin{gathered} y=-3-0.2 \\ \\ y=-3.2 \end{gathered}[/tex]Hence, the answers are:
• Standard Form:
[tex](x-5)^2=0.8(y+3)[/tex]• Value for "p":
[tex]p=0.2[/tex]• Vertex:
[tex](5,-3)[/tex]• Focus:
[tex](5,-2.8)[/tex]• Directrix:
[tex]y=-3.2[/tex]
Choose the graph of g(x) = |x-1| and its parent function f. Then choose the description of the
transformation.
Anya has 115 mangoes lauren has five times the the number of mangoes Anya has they put them together and sold them in the market at $450 to $15 the sold all the mangoes how much money was collected at the end of the sale
The total amount of money collected if Anya and Lauren sold their mangoes at $15 is $10,350
How to find total revenue made from selling the mangoes?Number of mangoes Anya has = 115 mangoesNumber of mangoes Lauren has = 5 × 115= 575 mangoes
Total number of mangoes = Number of mangoes Anya has + Number of mangoes Lauren has
= 115 + 575
= 690 mangoes
Amount each mangoes was sold = $15
Total amount of money collected = Total number of mangoes × Amount each mangoes was sold
= 690 × 15
= $10,350
So therefore, Anya and Lauren sold their total mangoes for $10,350
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Bill Gutierrez drove 130 miles at a speed of 65 miles per hour on an expressway for 2 hours. He drove 67.5 miles for 1.5 hours at 45 miles per hours on a state highway. What is his average speed?
Bill's average speed throughout his journey is 55mi/hr
Average Speed
The average speed Bill drove can be calculated using the formula of speed which is given as
[tex]speed = \frac{distance}{time}[/tex]
Substituting all the values into the equation, we can find the speed.
130 miles at 65mi/hr, 67.5miles at 1.5 hours and 45mi/hr.
[tex]average speed = \frac{65 + 45}{2} = \\speed = \frac{110}{2} = 55mi/hr[/tex]
The average speed at the end of the journey is 55mi/hr
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If f(x)= x2-5 and g(x)= -3x + 2, find f(g(x))
Answer:
D. 9x² - 12x - 1
Explanation:
To find f(g(x)), we need to replace x by g(x) as follows:
f(x) = x² - 5
f(g(x)) = (g(x))² - 5
Then, g(x) is equal to -3x + 2, so replacing g(x) by (-3x + 2), we get:
f(g(x)) = (g(x))² - 5
f(g(x)) = (-3x + 2)² - 5
f(g(x)) = (-3x)² + 2(-3x)(2) + 2² - 5
f(g(x)) = 9x² - 12x + 4 - 5
f(g(x)) = 9x² - 12x - 1
Therefore, the answer is D. 9x² - 12x - 1
Pls help I need work and a answer I have given an exsample
The original price of the jacket before sale amount is $45.
Original price of the jacket will be calculated by forming the expression relating mentioned price. Let us assume the original price of the jacket to be x.
Writing the equation representing original price, percentage and price after sale
80%×x = 36
Converting percentage to fraction
80/100×x = 36
Shifting the fraction to Right Hand Side of the equation
x = 36×100/80
Cancelling zero as it is common in numerator and denominator and performing division
x = 45
Therefore, according to the sale price, the original price of jacket is $45.
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Use the digits 1-9 to create 3 equivalent ratios. Each digit can only be used once. _:_=_ _:_=_ _:_ _
Equivalent ratios are the ratios that are the same when we compare them. Three equivalent ratios are 1/2, 4/8, 3/6 in digits from 1 to 9.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other
Equivalent ratios are the ratios that are the same when we compare them.
The digits from 1 to 9 include 1,2,3,4,5,6,7,8,9.
Ratios are nothing but fractions.
Let 1/2 (one by two) is the first ratio.
Now 3/6 (three by six) is the second ratio
4/8 (four by eight) is the third ratio.
If we calculate the value of 1/2 = 0.5
The value of 3/6=1/2=0.5
The value of 4/8= 1/2=0.5
we get the same answer for all the ratios 1/2, 4/8 and 3/6 that is 0.5
That is 0.5 or 1/2.
Hence the three equivalent ratios are 1/2, 4/8, 3/6.
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What value of n makes the equation true ?
8 × 0.25n = 2n
8 × -2 = -16
-0.5 × 8 = -4
-0.5 × -4n = 2n
2n - 16 + n= -4 + 2n
2n + n = 3n
3n - 16 = -4 + 2n
-2n -2n
n - 16 = -4
+16 +16
n = 12
Which are the foci of the ellipse represented by 25x^2 + 16y² = 400?
O (-3,0) and (3, 0)
O(-5, 0) and (5, 0)
O (0, 3) and (0, -3)
O (0, 5) and (0, -5)
The foci of the given ellipse are (D) (0, 5) and (0, -5).
What is an ellipse?In mathematics, an ellipse is a planar curve with two focal points, where the total of the two distances from any point on the curve to the focal points is a constant. It generalizes the shape of a circle, a unique variety of ellipse in which the two focus points coincide. For an ellipse with its center at (0,0) and its axes parallel to the coordinate axes, one point can be used to infer three more points. The other three points are (a,b), (a,b), and (a,b) if your point is (a,b).So, the foci of the ellipse are:
Equation is 25x² + 16y² = 400.Now, plot it on the graph as follows:(Refer to the graph attached below)
We can easily see that the coordinates on the y-axis are (0, 5) and (0, -5).Therefore, the foci of the given ellipse are (D) (0, 5) and (0, -5).
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The correct question is shown below:
Which are the foci of the ellipse represented by 25x² + 16y² = 400?
A. (-3,0) and (3, 0)
B. (-5, 0) and (5, 0)
C. (0, 3) and (0, -3)
D. (0, 5) and (0, -5)
The 20% off sale is a better deal than the $200 rebate or
$150 coupon for the $1,500 dining set. The Porters
budgeted $1,250 for a new dining room set. Explain why
this is the best deal for them. Are they under budget?
Answer:
20% off is better and it is the only offer which is under the budget.
20% off of the $1,500 dining set is $300, and the dining set price will be 1500 - 300 = $1200.
And by applying the $150 coupon, the dining set price will be $1500 - $150 = $1350.
Therefore 20% off is better and it is the only offer which is under the budget.
Step-by-step explanation:
Please help it’s due tomorrow morning
Explain the step that is used to solve the equation